: [pval, ks] = kolmogorov_smirnov_test (x, dist, params, alt)

Perform a Kolmogorov-Smirnov test of the null hypothesis that the sample x comes from the (continuous) distribution dist.

if F and G are the CDFs corresponding to the sample and dist, respectively, then the null is that F == G.

The optional argument params contains a list of parameters of dist. For example, to test whether a sample x comes from a uniform distribution on [2,4], use

kolmogorov_smirnov_test (x, "unif", 2, 4)

dist can be any string for which a function distcdf that calculates the CDF of distribution dist exists.

With the optional argument string alt, the alternative of interest can be selected. If alt is "!=" or "<>", the null is tested against the two-sided alternative F != G. In this case, the test statistic ks follows a two-sided Kolmogorov-Smirnov distribution. If alt is ">", the one-sided alternative F > G is considered. Similarly for "<", the one-sided alternative F > G is considered. In this case, the test statistic ks has a one-sided Kolmogorov-Smirnov distribution. The default is the two-sided case.

The p-value of the test is returned in pval.

If no output argument is given, the p-value is displayed.

Package: statistics